10) Horizontal beam supported on both ends - square profil 100 × 100 × 5, length is 800 mm.It is bent by the force in the middle of the beam by 0.2 mm. To achieve approximately half of the value of deflection,you will use the beam:

To calculate the required dimensions of the beam to achieve approximately half of the given deflection, we need to use the formula for deflection in a simply supported beam.

The formula for deflection in a simply supported beam under a point load applied at the center is given by:

δ = (F * L^3) / (48 * E * I)

Where:
δ = Deflection
F = Force applied
L = Length of the beam
E = Young's modulus of the material
I = Moment of inertia of the cross-section of the beam

To achieve approximately half of the given deflection, we can set up the following equation:

(0.2 mm / 2) = (F * L^3) / (48 * E * I)

Since the deflection will be halved, we can simplify the equation:

0.1 mm = (F * L^3) / (48 * E * I)

Now let's rearrange the equation to solve for I, the moment of inertia:

I = (F * L^3) / (48 * E * 0.1 mm)

Substituting the given values:
F = Unknown
L = 800 mm
E = Unknown
I = Unknown

We need the values of the force (F) and Young's modulus (E) to calculate the moment of inertia.

Please provide the force and the Young's modulus of the material used in the beam, so we can proceed with the calculation.